Method for predicting reservoir reform volume after vertical well volume fracturing of low-permeability oil/gas reservoir

ABSTRACT

The invention provides a method for predicting a reservoir reform volume after vertical well volume fracturing of a low-permeability oil/gas reservoir. The method sequentially includes the following steps: (1) calculating an induced stress produced by a hydraulic fracture in a three-dimensional space; (2) calculating a stratum pore pressure obtained after leak-off of fracturing fluid; (3) calculating a stratum pore elastic stress obtained after the leak-off of the fracturing fluid; (4) overlapping the stress fields obtained in the step (1), (2) and (3) with an original crustal stress field to obtain a new crustal stress field, and calculating the magnitude and direction of the overlapped three-direction effective principal stress in the reservoir space; (5) calculating an open fracturing determination coefficient M of a natural fracture in the reservoir space and a shear fracturing area determination coefficient S of the natural fracture.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is the national phase entry of InternationalApplication PCT/CN2017/082411, filed on Apr. 28, 2017, which is basedupon and claims priority to Chinese Patent Application No.201710280797.9, filed on Apr. 26, 2017, the entire contents of which areincorporated herein by reference.

TECHNICAL FIELD

The present invention belongs to the field of oil-gas field development,and in particular, to a method for predicting a reservoir reform volumeafter vertical well volume fracturing of a low-permeability oil/gasreservoir.

BACKGROUND

The low-permeability reservoir has poor physical properties, complexpore structure, low surface porosity and small throat, and therefore, anexpected yield-increasing effect is hardly achieved by a conventionalfracturing technology. The volume fracturing technology is an importanttechnological measure to reform a low-permeability oil/gas field andincrease the yield. Horizontal well volume fracturing is the maintechnical means for yield increase and reformation a low-permeabilityoil/gas reservoir. However, low-permeability oil/gas reservoirs in Chinaare dominated by continental deposits, and low-permeability reservoirsdeveloped in some oilfield blocks (such as some blocks in the ChangqingOilfield and Jilin Oilfield) are characterized by small reservoirforming areas, more longitudinal sublayers and small thickness.Therefore, the horizontal well volume reform technology shows someinadaptability, making the vertical well volume fracturing technologyapplied to the development of such reservoirs on a large scale. Accurateinterpretation results of fractured reservoir reform volume areconducive to reasonably evaluating the vertical well volume fracturingeffect, optimizing the fracturing construction design and accuratelypredicting the yield after fracturing. At present, the commonly usedmethods for on-site monitoring of a volume fractured fracture at homeand abroad include micro-seismic monitoring, inclinometer monitoring,and distributed acoustic sensing fracture monitoring. The micro-seismicmonitoring which is a widely used fracture monitoring method can be usedto detect the orientation, fracture length, fracture width, fractureheight and inclination angle of a complex fracture network body.However, this method has high technical cost and is not suitable forlarge-scale multi-well applications. If a reservoir reform volumemathematical model is used to predict the reservoir reform volume aftervolume fracturing, the cost can be greatly reduced. The existingreservoir reform volume prediction methods mainly include asemi-analysis method, a yield fitting method and a discrete fracturenetwork simulation method. The semi-analysis method and the yieldfitting method have higher requirements for basic data, so the formerneeds micro-seismic monitoring data of part of wells in the target blockfor performing calibration to obtain reliable prediction results, whilethe latter is necessary to predict the magnitude of the reservoir reformvolume based on yield data after fracturing. Although a discretefracture network simulation method does not need to obtain themicro-seismic monitoring data and the yield data after fracturing inadvance, but is relatively complex in basic theories, large incalculation amount, poor in model convergence and not easy to implement.Therefore, it can be seen that the existing method for predicting thereservoir reform volume has certain deficiencies and is thus notsuitable for large-scale application field practice.

To sum up, the currently required method for predicting a reservoirreform volume after vertical well volume fracturing of alow-permeability oil/gas reservoir should have the following twocharacteristics:(1) the requirements for basic data are relatively lowduring implementation, and the reservoir reform volume after volumefracturing can be directly predicted without the need to obtain a largeamount of basic data such as micro-seismic monitoring data and yielddata after fracturing in advance; (2) the basic theory is perfect, theidea is concise and intuitive, the operability is high, and accurateprediction results can be obtained.

SUMMARY

An objective of the present invention is to provide a method forpredicting a reservoir reform volume after vertical well volumefracturing of a low-permeability oil/gas reservoir. The method of thepresent invention which is used for predicting the reservoir reformvolume after vertical well volume fracturing is better in operabilityand accuracy, provides a favorable theoretical basis for effectevaluation and yield prediction after vertical well volume fracturing ofthe low-permeability oil/gas reservoir, and overcomes the defects of theprior art.

To fulfill said technical objective, the present invention provides thefollowing technical solution.

First, a crustal stress field calculation model under athree-dimensional hydraulic fracture interference mode is established,i.e., calculating an induced stress produced by a hydraulic fracture atany point in a three-dimensional space, a stratum pore pressure obtainedafter leak-off of fracturing fluid and a pore elastic stressrespectively, and overlapping the three stress fields with an originalcrustal stress field based on the basic theory of elastic mechanics toobtain a crustal stress field under the three-dimensional hydraulicfracture interference mode; secondly, the magnitude and direction ofthree-direction effective principal stress under the three-dimensionalhydraulic fracture interference mode are calculated; at last, under acomplex crustal stress field with three-dimensional hydraulic fractureinterference, whether a natural fracture in the reservoir space isopened or fractured by shearing is calculated and analyzed, and thetotal swept volume of the two fracture ways is equivalent to thereservoir reform volume.

A method for predicting a reservoir reform volume after vertical wellvolume fracturing of a low-permeability oil/gas reservoir sequentiallycomprises the following steps:

(1) calculating an induced stress produced by a hydraulic fracture in athree-dimensional space. Based on the three-dimensional displacementdiscontinuity theory, a three-dimensional hydraulic fracture inducedstress field calculation model is established (Wu K. Numerical modelingof complex hydraulic fracture development in unconventional reservoirs[D]. The University of Texas at Austin, 2014). The magnitude of aninduced stress produced by a hydraulic fracture at any point i in athree-dimensional space is calculated according to the followingcalculation formula:

$\begin{matrix}{\quad\left\{ \begin{matrix}{\sigma_{xx}^{i} = {{\sum\limits_{j = 1}^{N}\; {F_{{xx},{sL}}^{i,j}D_{sL}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{xx},{sH}}^{i,j}D_{sH}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{xx},{nn}}^{i,j}D_{n}^{j}}}}} \\{\sigma_{yy}^{i} = {{\sum\limits_{j = 1}^{N}\; {F_{{yy},{sL}}^{i,j}D_{sL}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{yy},{sH}}^{i,j}D_{sH}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{yy},{nn}}^{i,j}D_{n}^{j}}}}} \\{\sigma_{zz}^{i} = {{\sum\limits_{j = 1}^{N}\; {F_{{zz},{sL}}^{i,j}D_{sL}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{zz},{sH}}^{i,j}D_{sH}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{zz}.{nn}}^{i,j}D_{n}^{j}}}}} \\{\sigma_{xy}^{i} = {{\sum\limits_{j = 1}^{N}\; {F_{{xy},{sL}}^{i,j}D_{sL}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{xy},{sH}}^{i,j}D_{sH}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{xy},{nn}}^{i,j}D_{n}^{j}}}}} \\{\sigma_{xz}^{i} = {{\sum\limits_{j = 1}^{N}\; {F_{{xz},{sL}}^{i,j}D_{sL}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{xz},{sH}}^{i,j}D_{sH}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{xz},{nn}}^{i,j}D_{n}^{j}}}}} \\{\sigma_{yz}^{i} = {{\sum\limits_{j = 1}^{N}\; {F_{{yz},{sL}}^{i,j}D_{sL}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{yz},{sH}}^{i,j}D_{sH}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{yz},{nn}}^{i,j}D_{n}^{j}}}}}\end{matrix} \right.} & (1) \\\left\{ {\begin{matrix}{\sigma_{zz}^{j} = p_{net}^{j}} \\{\sigma_{xz}^{j} = 0} \\{\sigma_{yz}^{j} = 0}\end{matrix}\left( {{j = 1},2,3,\ldots \mspace{11mu},N} \right)} \right. & (2)\end{matrix}$

in the formulas:

σ_(xx) ^(i), σ_(yy) ^(i), σ_(zz) ^(i), σ_(xy) ^(i), σ_(yz) ^(i) arepositive induced stresses and shear induced stresses produced by thehydraulic fracture at any point i in the three-dimensional spacerespectively, MPa;

F_(xx,sL) ^(i,j), F_(xx,sH) ^(i,j), F_(xx,nn) ^(i,j), F_(yy,sL) ^(i,j),F_(yy,sH) ^(i,j), F_(yy,nn) ^(i,j), F_(zz,sL) ^(i,j), F_(zz,sH) ^(i,j),F_(zz,nn) ^(i,j), F_(xy,sL) ^(i,j), F_(xy,sH) ^(i,j), F_(xy,nn) ^(i,j),F_(xz,sL) ^(i,j), F_(xz,sH) ^(i,j), F_(xz,nn) ^(i,j), F_(yz,sL) ^(i,j),F_(yz,sH) ^(i,j) and F_(yz,nn) ^(i,j) are boundary influencecoefficients respectively;

N is a total number of units divided by the hydraulic fracture;

D_(sL) ^(j), D_(sH) ^(j) and D_(n) ^(j) are discontinuity quantities oftangential and normal displacements on the hydraulic fracture unit jrespectively, which can be reversely derived from a condition given in(2) in combination with a formula (1);

σ_(zz) ^(i) is a positive stress boundary value in the original minimumcrustal stress direction (parallel to z-axis) on the hydraulic fractureunit j, which is generally a net pressure suffered by the hydraulicfracture wall, MPa;

σ_(xz) ^(j) and σ_(yz) ^(i) are boundary values of shear stresses on thehydraulic fracture unit j respectively, generally 0, MPa;

P_(net) ^(j) is a net pressure on the hydraulic fracture unit j, MPa.

(3) Calculating a stratum pore pressure obtained after leak-off offracturing fluid. The permeability of a low-permeability reservoirmatrix is extremely low, so the leak-off of fracturing fluid to thematrix can be ignored. Under normal circumstances, the natural fracturesdeveloped in the reservoir serve as main channels for leak-off offracturing fluid. In the low-permeability reservoir, only the leak-offbehavior of the fracturing fluid along the natural fractures isconsidered. Due to the differences in the original fluid properties ofthe stratum and the structural characteristics of the reservoir rock,different methods are used in a low-permeability oil reservoir and alow-permeability gas reservoir to calculate the stratum pore pressurechange values caused by leak-off of fracturing fluid. The specificcalculation formulas (Warpinski N R, Wolhart S L, Wright C A. Analysisand Prediction of Microseismicity Induced by Hydraulic Fracturing [J].SPE Journal, 2004, 9(01): 24-33) are as follows:

for the low-permeability oil reservoir:

$\begin{matrix}\left\{ \begin{matrix}{P^{i} = {P_{0} + {\left( {P_{f} - P_{0}} \right)e^{- {{\xi\lambda}{({1 + \sqrt{\mu + b^{2}}})}}}}}} \\{\xi = \left( \frac{g\; \pi}{2} \right)^{2}} \\{g = \sqrt{\frac{{\varphi\mu}_{l}c}{kt}}}\end{matrix} \right. & (3)\end{matrix}$

for the low-permeability gas reservoir:

$\begin{matrix}{\quad\left\{ {\begin{matrix}{P^{i} = {P_{o} + {\left( {P_{f} - P_{o}} \right)\frac{\eta}{\eta_{L}}}}} \\{\eta_{L} = \sqrt{\frac{2{k\left( {P_{f} - P_{o}} \right)}t}{\mu_{l}\; \varphi \; L^{2}}}} \\{\eta = {{ar}\; {\sinh \left( \sqrt{\frac{x_{i}^{2} + y_{i}^{2} - L^{2} + \sqrt{\left( {L^{2} - x_{i}^{2} - y_{i}^{2}} \right)^{2} + {4L^{2}y_{i}^{2}}}}{2L^{2}}} \right)}}}\end{matrix};} \right.} & (4)\end{matrix}$

in the formulas:

P^(i) is a pore pressure at any point i in the stratum after leak-off offracturing fluid, MPa;

P^(o) is an original pore pressure of the stratum, MPa;

P_(f)is a fluid pressure in the hydraulic fracture, MPa;

λ, μ is a coordinate value of any leak-off point i in athree-dimensional hydraulic fracture ellipsoidal coordinate system, m²;

b is a half fracture height of the hydraulic fracture at a wellbore, m;

φ is porosity of the natural fracture, no dimension;

μ_(l) is the viscosity of fracturing fluid, mPa·s;

c is a compression factor of the natural fracture, MPa⁻¹;

k is permeability of the reservoir, D;

t is leak-off time, s;

L is a length of the hydraulic fracture, m;

x_(i) is a coordinate value of any leak-off point i in athree-dimensional rectangular coordinate system along the fracturelength (x-axis direction), m;

y_(i) is a coordinate value of any leak-off point i in thethree-dimensional rectangular coordinate system along the fractureheight direction (y-axis direction), m.

(3) calculating a stratum pore elastic stress obtained after leak-off offracturing fluid. The leak-off of fracturing fluid will increase thepore pressure in the local reservoir, and will disturb the stress aroundthe hydraulic fracture. In the low-permeability gas reservoir, theinfluence of the pore elastic stress can be neglected, but in the oilreservoir, this pore elastic stress cannot be neglected, and can becalculated according to the formula (Smith MB. Stimulation design forshort, precision hydraulic fractures [J]. Society of Petroleum EngineersJournal, 1985, 25(03):371-379):

$\begin{matrix}{\quad\left\{ {\begin{matrix}{{\Delta\sigma}^{i} = \frac{A\left( {P^{i} - P_{o}} \right)}{2 + \varsigma}} \\{A = {\alpha \frac{1 - {2v}}{1 - v}}} \\{\varsigma = \frac{{\gamma \; h\sqrt{\pi}} + \sqrt{{\gamma^{2}h^{2}\pi} + 4}}{2}} \\{\gamma = \sqrt{\frac{10^{3} \times {\varphi\mu}\; c}{4{kt}}}}\end{matrix};} \right.} & (5)\end{matrix}$

in the formula:

Δσ^(i) is a pore elastic stress produced by a change in the stratum porepressure at any point i, MPa;

A is a pore elastic constant, no dimension;

v is a Poisson's ratio of stratum rock, no dimension;

ç is a parameter for describing the dimension and shape of fluidintrusion, no dimension;

α is a Biot coefficient, no dimension;

h is a half fracture height of the natural fracture, m.

(4) Overlapping the above three stress fields with an original crustalstress field to obtain a new crustal stress field, and calculating themagnitude and direction of the overlapped three-direction effectiveprincipal stress in the reservoir space. First, the three induced stressfields are overlapped with the original crustal stress field based onthe basic theory of elastic mechanics, and the calculation formula is asfollows:

$\begin{matrix}\left\{ {\begin{matrix}{\sigma_{xxT} = {\sigma_{xx} + \sigma_{H} + {\alpha \; P} + {\Delta\sigma}}} \\{\sigma_{yyT} = {\sigma_{yy} + \sigma_{V} + {\alpha \; P} + {\Delta\sigma}}} \\{\sigma_{zzT} = {\sigma_{zz} + \sigma_{h} + {\alpha \; P} + {\Delta\sigma}}} \\{\sigma_{xyT} = \sigma_{xy}} \\{\sigma_{xzT} = \sigma_{xz}} \\{\sigma_{yzT} = \sigma_{yz}}\end{matrix}.} \right. & (6)\end{matrix}$

Secondly, equation (6) is substituted into equation (7) and equation (7)is solved to obtain the magnitude of the three-direction effectiveprincipal stress in the reservoir space after the stress fields areoverlapped.

σ_(i) ³+(σ_(xxT)+σ_(yyT)+σ_(zzT)) σ_(i)²+(σ_(xxT)σ_(yyT)+σ_(xxT)σ_(zzT)+σ_(yyT)σ_(zzT)−σ_(xyT) ²−σ_(xzT)²−σ_(yzT) ²) σ_(i)−(σ_(xxT)σ_(yyT)σ_(zzT)−σ_(xxT)σ_(yzT)²−σ_(yyT)σ_(zxT) ²−σ_(zzT)σ_(xyT) ²+2σ_(xyT)σ_(xzT)σ_(yzT))=0 (i=1,2,3)  (7).

Then, the direction of the three-direction effective principal stress inthe reservoir space after the stress fields are overlapped is calculatedaccording to the following calculation formula:

$\begin{matrix}\left\{ {{\begin{matrix}{\beta_{xi} = {\arccos \left( \frac{A_{i}}{\sqrt{A_{i} + B_{i} + C_{i}}} \right)}} \\{\beta_{yi} = {\arccos \left( \frac{B_{i}}{\sqrt{A_{i} + B_{i} + C_{i}}} \right)}} \\{\beta_{zi} = {\arccos \left( \frac{C_{i}}{\sqrt{A_{i} + B_{i} + C_{i}}} \right)}} \\{A_{i} = {{\sigma_{xyT}\sigma_{yzT}} - {\sigma_{xzT}\left( {\sigma_{yyT} - \sigma_{i}} \right)}}} \\{B_{i} = {{\sigma_{xzT}\sigma_{xyT}} - {\sigma_{yzT}\left( {\sigma_{xxT} - \sigma_{i}} \right)}}} \\{C_{i} = {{\left( {\sigma_{yyT} - \sigma_{i}} \right)\left( {\sigma_{xxT} - \sigma_{i}} \right)} - \sigma_{xyT}^{2}}}\end{matrix}\left( {{i = 1},2,3} \right)};} \right. & (8)\end{matrix}$

in the formula:

σ_(xx) is an induced stress produced by the hydraulic fracture in theoriginal maximum horizontal crustal stress direction (parallel to x-axisdirection), and the specific stress value at each point is σ_(xx) ^(i),MPa;

σ_(yy) is an induced stress produced by the hydraulic fracture in theoriginal vertical crustal stress direction (parallel to y-axisdirection), and the specific stress value at each point is σ_(yy) ^(i),MPa;

σ_(zz) is an induced stress produced by the hydraulic fracture in theoriginal minimum horizontal crustal stress direction (parallel to z-axisdirection), and the specific stress value at each point is σ_(zz) ^(i),MPa;

σ_(xy), σ_(xz), and σ_(yz) are shear induced stresses produced by thehydraulic fracture, and the specific stress value at each point isσ_(xy) ^(i), σ_(xz) ^(i), σ_(yz) ^(i) respectively, MPa;

P is a pore pressure in the stratum after leak-off of fracturing fluid,and the specific stress at each point is P^(i), MPa;

Δσ is a pore elastic stress in the stratum after leak-off of fracturingfluid, and the specific stress value at each point is Δσ^(i), MPa;

σ_(h) is an original minimum horizontal crustal stress, MPa;

σ_(H) is an original maximum horizontal crustal stress, MPa;

σ_(V) is an original vertical crustal stress, MPa;

σ_(i)(i=1, 2, 3) is the magnitude of the three-direction principleeffective stress in the reservoir space after the above three stressfields are overlapped with the original crustal stress field, whereσ1>σ2>σ3, MPa;

β_(xi), β_(yi), and β_(zi) (i=1, 2, 3) are included angles betweenrespective directions of effective principal stress σ_(i)(i=1, 2, 3) inthe reservoir space after the above three stress fields are overlappedwith the original crustal stress field and the x-axis direction, they-axis direction and the z-axis direction respectively, 0° to 90°.

All calculations in the present invention are positive with compressivestress and negative with tensile stress.

(5) Calculating an open fracturing determination coefficient M of thenatural fracture in the reservoir space and a shear fracturing areadetermination coefficient S of the natural fracture so as to predict thereservoir reform volume after volume fracturing, and determining thelength, width and height of the volume to obtain the magnitude of thereservoir reform volume. The development of natural fractures is anecessary condition for obtaining the ideal volume fracturing reformeffect for the low-permeability oil/gas reservoir. Natural fractures arethe weak links in the reservoir mechanics. During the reservoirfracturing reform process, natural fractures are more likely to open orfracture by shearing prior to bedrocks, thus forming a complex fracturenetwork body in the three-dimensional reservoir space. Therefore, thetotal swept volume of these two fracturing ways can be equivalent to thereservoir reform volume. Due to the complex form of reservoir reformvolume, in order to facilitate the calculation of the magnitude of thereservoir reform volume, the reservoir reform volume is equivalent to acuboid in accordance with the conventional calculation thought at thepresent stage. The magnitude of the reservoir reform volume iscalculated by a way of calculating the volume of the cuboid (“length xwidth x height”).

M is an open fracturing determination coefficient of the naturalfracture, and M>0 refers that the natural fracture will be opened andfractured in the hydraulic fracturing process, the calculation formulathereof being as follows:

$\quad\begin{matrix}{\mspace{770mu} (9)} \\\left\{ {{\begin{matrix}{M = {- \sigma_{n}}} \\{\sigma_{n} = {{\left( {{\sigma_{2}\cos^{2}\theta} + {\sigma_{3}\sin^{2}\theta}} \right)\sin^{2}\phi} + {\sigma_{1}\cos^{2}\phi}}} \\{\phi = {\arccos \left( {n_{1},{nf}} \right)}} \\{\theta = {\arctan \left( \frac{\cos \left( {n_{3},{nf}} \right)}{\cos \left( {n_{2},{nf}} \right)} \right)}} \\{{\cos \left( {n_{i},{nf}} \right)} = {{\cos \; \beta_{xi}\sin \; {\alpha sin\vartheta}} + {\cos \; \beta_{yi}\cos \; \alpha} + {\cos \; \beta_{zi}\sin \; {\alpha cos\vartheta}}}}\end{matrix}\left( {{i = 1},2,3} \right)};} \right.\end{matrix}$

S is a shear fracturing area determination coefficient of the naturalfracture, and S>0 refers that the natural fracture will be fractured byshearing in the hydraulic fracturing process, the calculation formulabeing as follows:

$\begin{matrix}\left\{ {\begin{matrix}{S = {\tau - {k_{f}\sigma_{n}} - \sigma_{o}}} \\{\tau = \sqrt{{\left( {{\sigma_{2}^{2}\cos^{2}\theta} + {\sigma_{3}^{2}\sin^{2}\theta}} \right)\sin^{2}\phi} + {\sigma_{1}^{2}\cos^{2}\phi} - \sigma_{n}^{2}}}\end{matrix};} \right. & (10)\end{matrix}$

in the formula:

σ_(n) is a positive stress of the natural fracture wall, MPa;

ψ is an included angle between the normal vector of the natural fracturesurface and the maximum effective principal stress σ_(i) after thestress fields are overlapped, 0⁰ to 90°;

θ is an included angle between the normal vector of the natural fracturesurface and the minimum effective principal stress σ₃ after the stressfields are overlapped, 0° to 90°;

α is an included angle between an inclination angle of the naturalfracture, i.e., the normal vector of the natural fracture surface andthe y-axis, 0° to 90°;

ϑ is an included angle between the natural fracture trend and theoriginal maximum horizontal crustal stress (x-axis direction), 0° to90°;

τis a shear stress suffered by the natural fracture surface, MPa;

K_(f) is a friction coefficient of the natural fracture wall, nodimension;

σ_(o) is a cohesive force of the natural fracture, MPa.

The total swept volume of S>0 and M>0 in the reservoir space is thereservoir reform volume after vertical well volume fracturing, thelength, width and height of the volume are determined by observing a topview and a side view of the reservoir reform volume, and the magnitudeof the reservoir reform volume is obtained by a way of“length×width×height”.

The calculation formulas and parameters involved in the presentinvention are numerous, and, it will be too burdensome if they arelisted one by one. In order to ensure that the present invention issimple and intuitive, only the main calculation formulas and parametersare listed, and corresponding reference documents are listed for thecalculation formulas and parameters that are not given.

Compared with the prior art, the present invention has the followingbeneficial effects: based on the basic theory of elastic mechanics andthe three-dimensional displacement discontinuity theory, a complexcrustal stress field calculation model taking a three-dimensionalhydraulic fracture interference mode into consideration is established,the open fracturing and shear fracturing behaviors of the naturalfracture under the complex crustal stress condition are calculated andanalyzed, the total swept volume of the above two fracturing modes isequivalent to the reservoir reform volume based on the mechanicsformation mechanism of the reservoir reform volume after volumefracturing, and a method for predicting a reservoir reform volume aftervertical well volume fracturing of a low-permeability oil/gas reservoiris provided; (2) this method is concise and intuitive, has strongimplementability, and is not necessary to obtain micro-seismicmonitoring data or yield data after fracturing in advance when thereservoir reform volume is predicted, thereby remedying thedeficienciesof the existing calculation methods having higher requirements for basicdata.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of divisions of units of a hydraulicfracture based on a three-dimensional displacement discontinuity method.

FIG. 2 is a top view of prediction results of the method and a top viewof micro-seismic event monitoring results after a Q30 well is fractured.

FIG. 3 is a side view of prediction results of the method and a sideview of micro-seismic event monitoring results after a Q30 well isfractured.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The present invention is further described below in detail incombination with the drawings and the field application examples.

Taking a tight sandstone reservoir vertical well (Q30) in an oil fieldin the East of China as an example, the well has a total depth of 2550m, a reservoir depth of 2442.4-2446.2 m, a thickness of 3.8m, an averageoil layer porosity of 9.2%, and an average permeability of 0.62 mD, andis of a low-porosity, low-permeability reservoir. A technical means of alarge-displacement, low-sand-ratio, large-volume, low-viscosity fluidsystem (based on slickwater) is adopted for this well to perform volumefracturing, such that the reservoir reform volume is maximized and thereservoir utilization ratio is increased, thereby increasing theper-well yield. The natural fracture in the reservoir develops with alarger fracture inclination angle of about 80 degrees, and an includedangle with the maximum horizontal crustal stress direction of about 15degrees. Other basic parameters are shown in Table 1 below.

TABLE 1 Basic Parameter List of Q30 well Horizontal maximum crustal 49Horizontal minimum 38.5 stress, MPa crustal stress, MPa Vertical crustalstress, MPa 55 Biot Coefficient 1 Design height of hydraulic 50 Halflength of hydraulic 150 fracture at wellhole, m fracture design, mPoisson's ratio 0.2 Original pore pressure 26.8 of stratum, MPa YoungModulus of stratum 28 Cohesive force of 0 rock, GPa natural fracture,MPa Net pressure of hydraulic 5 Compression coefficient, 2.15 fracture,MPa 10⁻⁴MPa⁻¹ Viscosity of leak-off 1 Permeability of natural 150fracturing fluid fracture, mD (mPa · s) Friction coefficient of 0.6Leak-off time, min 150 natural fracture wall Porosity in naturalfracture 0.2 Height of natural 10 fracture, m

Step 1, calculating an induced stress produced by a hydraulic fracturein a three-dimensional stratum space using the data in Table 1 andFormulas (1) and (2). FIG. 1 shows a specific manner for divisions ofunits of the hydraulic fracture according to a three-dimensionaldisplacement discontinuity method, as well as a positive induced stressand a tangential induced stress produced by the hydraulic fracture atany point i in the stratum.

Step 2, calculating a stratum pore pressure after leak-off of fracturingfluid using the data in Table 1 and Formula (3) (using Formula (4) incase of a low-permeability gas reservoir).

Step 3, calculating a stratum pore elastic stress after leak-off offracturing fluid using the data in Table 1 and Formula (5) (the stratumpore elastic stress caused by leak-off of fracturing fluid can beneglected in case of a low-permeability gas reservoir).

Step 4, calculating the magnitude and direction of a spatialthree-direction effective principal stress of a new crustal stress fieldafter the above three stress fields are overlapped with the originalcrustal stress using the data in Table 1 and Formulas (6)-(8) incombination with the calculation results of Steps 1 to 3.

Step 5, predicting a reservoir reform volume of the oil well Q30 aftervolume fracturing using the data in Table 1 and Formulas (9)-(10) incombination with the calculation result of Step 4, determining thelength, width and height of the reservoir reform volume by observing thetop view and the side view of the reservoir reform volume, andcalculating the magnitude of the reservoir reform volume by a way of“length×width×height”.

As observed from FIG. 2 and FIG. 3, upon calculation in the above steps,it is predicted that the magnitude of the reservoir reform volume of theQ30 well after volume fracturing is approximately 154×10⁴ m³ (length 300m, width 78 m, height 66 m). After the completion of fracturing of theQ30 well, a micro-seismic monitoring interpretation result shows that acomplex fracture network body with a volume reformed as approximately141×10⁴ m³ (length 300 m, width 76 m, height 62 m) is formed in thereservoir, which is very close to the prediction result of the presentinvention. At the same time, the top view and the side view of themicro-seismic event monitoring result of the Q30 well after fracturingbasically coincides with the top view and the side view of theprediction result of the present method. It is indicated that the methodfor predicting the reservoir reform volume after vertical well volumefracturing of the low-permeability oil/gas reservoir proposed by thepresent invention is relatively reasonable, and can provide favorablereferences for the optimization design of reservoir fracturingconstruction parameters, the evaluation of effects after fracturing, andthe accurate yield prediction after fracturing.

What is claimed is:
 1. A method for predicting a reservoir reform volumeafter vertical well volume fracturing of a low-permeability oil/gasreservoir, sequentially comprising the following steps: (1) calculatingan induced stress produced by a hydraulic fracture in athree-dimensional space to obtain a first induced stress field; (2)calculating a stratum pore pressure obtained after leak-off offracturing fluid to obtain a second induced stress field; (3)calculating a stratum pore elastic stress obtained after the leak-off ofthe fracturing fluid to obtain a third induced stress field; (4)overlapping the first, second and third induced stress fields with anoriginal crustal stress field to obtain a new crustal stress field, andcalculating a magnitude and a direction of an overlapped three-directioneffective principal stress in a reservoir space; and (5) calculating anopen fracturing determination coefficient M of a natural fracture in thereservoir space and a shear fracturing area determination coefficient Sof the natural fracture so as to predict the reservoir reform volumeafter volume fracturing, and determining a length, a width and a heightof the reservoir reform volume to obtain a magnitude of the reservoirreform volume.
 2. The method for predicting the reservoir reform volumeafter vertical well volume fracturing of the low-permeability oil/gasreservoir according to claim 1, wherein calculating the induced stressproduced by the hydraulic fracture in the three-dimensional space inStep (1) refers to establishing a three-dimensional hydraulic fractureinduced stress field calculation model based on a three-dimensionaldisplacement discontinuity theory, and calculating a magnitude of aninduced stress produced by the hydraulic fracture at a point i in thethree-dimensional space according to the following calculation formula:$\begin{matrix}\left\{ \begin{matrix}{\sigma_{xx}^{i} = {{\sum\limits_{j = 1}^{N}\; {F_{{xx},{sL}}^{i,j}D_{sL}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{xx},{sH}}^{i,j}D_{sH}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{xx},{nn}}^{i,j}D_{n}^{j}}}}} \\{\sigma_{yy}^{i} = {{\sum\limits_{j = 1}^{N}\; {F_{{yy},{sL}}^{i,j}D_{sL}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{yy},{sH}}^{i,j}D_{sH}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{yy},{nn}}^{i,j}D_{n}^{j}}}}} \\{\sigma_{zz}^{i} = {{\sum\limits_{j = 1}^{N}\; {F_{{zz},{sL}}^{i,j}D_{sL}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{zz},{sH}}^{i,j}D_{sH}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{zz}.{nn}}^{i,j}D_{n}^{j}}}}} \\{\sigma_{xy}^{i} = {{\sum\limits_{j = 1}^{N}\; {F_{{xy},{sL}}^{i,j}D_{sL}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{xy},{sH}}^{i,j}D_{sH}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{xy},{nn}}^{i,j}D_{n}^{j}}}}} \\{\sigma_{xz}^{i} = {{\sum\limits_{j = 1}^{N}\; {F_{{xz},{sL}}^{i,j}D_{sL}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{xz},{sH}}^{i,j}D_{sH}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{xz},{nn}}^{i,j}D_{n}^{j}}}}} \\{\sigma_{yz}^{i} = {{\sum\limits_{j = 1}^{N}\; {F_{{yz},{sL}}^{i,j}D_{sL}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{yz},{sH}}^{i,j}D_{sH}^{j}}} + {\sum\limits_{j = 1}^{N}\; {F_{{yz},{nn}}^{i,j}D_{n}^{j}}}}}\end{matrix} \right. \\\left\{ {{\begin{matrix}{\sigma_{zz}^{j} = p_{net}^{j}} \\{\sigma_{xz}^{j} = 0} \\{\sigma_{yz}^{j} = 0}\end{matrix}\left( {{j = 1},2,3,\ldots \mspace{11mu},N} \right)};} \right.\end{matrix}$ in the formulas, σ_(xx) ^(i), σ_(yy) ^(i), σ_(zz) ^(i),σ_(xy) ^(i), σ_(xz) ^(i), σ_(yz) ^(i) are positive induced stresses andshear induced stresses produced by the hydraulic fracture at the point iin the three-dimensional space respectively, MPa; F_(xx,sL) ^(i,j),F_(xx,sH) ^(i,j), F_(xx,nn) ^(i,j), F_(yy,sL) ^(i,j), F_(yy,sH) ^(i,j),F_(yy,nn) ^(i,j), F_(zz,sL) ^(i,j), F_(zz,sH) ^(i,j), F_(zz,nn) ^(i,j),F_(xy,sL) ^(i,j), F_(xy,sH) ^(i,j), F_(xy,nn) ^(i,j), F_(xz,sL) ^(i,j),F_(xz,sH) ^(i,j), F_(xx,nn) ^(i,j), F_(yz,sL) ^(i,j), F_(yz,Sh) ^(i,j)and F_(yz,nn) ^(i,j) are boundary influence coefficients respectively; Nis a total number of units divided by the hydraulic fracture; D_(sL)^(j), D_(sH) ^(j) and D_(n) ^(j) are discontinuity quantities oftangential and normal displacements on hydraulic fracture unit jrespectively; σ_(zz) ^(i) is a positive stress boundary value in anoriginal minimum crustal stress direction (parallel to a z-axis) on thehydraulic fracture unit j, MPa; σ_(xz) ^(i) and σ_(yz) ^(i) are boundaryvalues of shear stresses on the hydraulic fracture unit j respectively,generally 0, MPa; p_(net) ^(j) is a net pressure on the hydraulicfracture unit j, MPa.
 3. The method for predicting the reservoir reformvolume after vertical well volume fracturing of the low-permeabilityoil/gas reservoir according to claim 1, wherein in Step (2), the stratumpore pressure is calculated after the leak-off of the fracturing fluidaccording to the specific calculation formula: for the low-permeabilityoil reservoir: $\quad\left\{ \begin{matrix}{P^{i} = {P_{0} + {\left( {P_{f} - P_{0}} \right)e^{- {{\xi\lambda}{({1 + \sqrt{\mu + b^{2}}})}}}}}} \\{\xi = \left( \frac{g\; \pi}{2} \right)^{2}} \\{g = \sqrt{\frac{{\varphi\mu}_{l}c}{kt}}}\end{matrix} \right.$ for the low-permeability gas reservoir:$\begin{matrix}{P^{i} = {P_{o} + {\left( {P_{f} - P_{o}} \right)\frac{\eta}{\eta_{L}}}}} \\{\eta_{L} = \sqrt{\frac{2{k\left( {P_{f} - P_{o}} \right)}t}{\mu_{l}\; \varphi \; L^{2}}}} \\{\eta = {{ar}\; {\sinh \left( \sqrt{\frac{x_{i}^{2} + y_{i}^{2} - L^{2} + \sqrt{\left( {L^{2} - x_{i}^{2} - y_{i}^{2}} \right)^{2} + {4L^{2}y_{i}^{2}}}}{2L^{2}}} \right)}}}\end{matrix};$ in the formulas: p^(i) is a pore pressure at any point iin a stratum after the leak-off of the fracturing fluid, MPa; P₀ is anoriginal pore pressure of the stratum, MPa; P_(f)is a fluid pressure inthe hydraulic fracture, MPa; λ, ν is a coordinate value of any leak-offpoint i in a three-dimensional hydraulic fracture ellipsoidal coordinatesystem, m²; b is a half fracture height of the hydraulic fracture at awellbore, m; φ is porosity of the natural fracture, no dimension; μ_(i)is viscosity of the fracturing fluid, mPa·s; c is a compression factorof the natural fracture, MPa⁻¹; k is permeability of the reservoir, D; tis leak-off time, s; L is a length of the hydraulic fracture, m; x_(i)is a coordinate value of any leak-off point i in a three-dimensionalrectangular coordinate system along the fracture length (an x-axisdirection), m; y_(i) is a coordinate value of any leak-off point i inthe three-dimensional rectangular coordinate system along the fractureheight direction (a y-axis direction), m.
 4. The method for predictingthe reservoir reform volume after vertical well volume fracturing of thelow-permeability oil/gas reservoir according to claim 1, wherein in Step(3), the stratum pore elastic stress after the leak-off of thefracturing fluid is calculated according to the following calculationformula: $\left\{ {\begin{matrix}{{\Delta\sigma}^{i} = \frac{A\left( {P^{i} - P_{o}} \right)}{2 + \varsigma}} \\{A = {\alpha \frac{1 - {2v}}{1 - v}}} \\{\varsigma = \frac{{\gamma \; h\sqrt{\pi}} + \sqrt{{\gamma^{2}h^{2}\pi} + 4}}{2}} \\{\gamma = \sqrt{\frac{10^{3} \times {\varphi\mu}\; c}{4{kt}}}}\end{matrix};} \right.$ in the formula: Δσ^(i) is a pore elastic stressproduced by a change in the stratum pore pressure at any point i, MPa; Ais a pore elastic constant, no dimension; v is a Poisson's ratio ofstratum rock, no dimension; ç is a parameter for describing a dimensionand a shape of fluid intrusion, no dimension; α is a Biot coefficient,no dimension; h is a half fracture height of the natural fracture, m. 5.The method for predicting the reservoir reform volume after verticalwell volume fracturing of the low-permeability oil/gas reservoiraccording to claim 1, wherein in Step (4), the magnitude and directionof the three-direction effective principal stress in the reservoir spaceafter the first, second and third induced stress fields are overlappedis calculated according to the following processes: first, the first,second and third induced stress fields are overlapped with the originalcrustal stress field: $\left\{ {\begin{matrix}{\sigma_{xxT} = {\sigma_{xx} + \sigma_{H} + {\alpha \; P} + {\Delta\sigma}}} \\{\sigma_{yyT} = {\sigma_{yy} + \sigma_{V} + {\alpha \; P} + {\Delta\sigma}}} \\{\sigma_{zzT} = {\sigma_{zz} + \sigma_{h} + {\alpha \; P} + {\Delta\sigma}}} \\{\sigma_{xyT} = \sigma_{xy}} \\{\sigma_{xzT} = \sigma_{xz}} \\{\sigma_{yzT} = \sigma_{yz}}\end{matrix};} \right.$ said formula is substituted into the followingformula solved to obtain the magntitude of the three-direction effectiveprincipal stress in the reservoir space after the first second and thirdinduced stress fields are overlapped:σ_(i) ³−(σ_(xxT)+σ_(yyT)+σ_(zzT)) σ_(i)²(σ_(xxT)σ_(yyT)+σ_(xxT)σ_(zzT)+σ_(yyT)σ_(zzT)−σ_(xyT) ²−σ_(xzT)²−σ_(yzT) ²) σ_(i)−(σ_(xxT)σ_(yyT)σ_(zzT)−σ_(xxT)σ_(yzT)²−σ_(yyT)σ_(zxT) ²−σ_(zzT)σ_(xyT) ²+2σ_(xyT)σ_(xzT)σ_(yzT))=0 (i=1,2,3);then, the direction of the three-direction effective principal stress inthe reservoir space after the first, second and third induced stressfields are overlapped is calculated according to the followingcalculation formula: $\begin{matrix}\left\{ {{\begin{matrix}{\beta_{xi} = {\arccos \left( \frac{A_{i}}{\sqrt{A_{i} + B_{i} + C_{i}}} \right)}} \\{\beta_{yi} = {\arccos \left( \frac{B_{i}}{\sqrt{A_{i} + B_{i} + C_{i}}} \right)}} \\{\beta_{zi} = {\arccos \left( \frac{C_{i}}{\sqrt{A_{i} + B_{i} + C_{i}}} \right)}} \\{A_{i} = {{\sigma_{xyT}\sigma_{yzT}} - {\sigma_{xzT}\left( {\sigma_{yyT} - \sigma_{i}} \right)}}} \\{B_{i} = {{\sigma_{xzT}\sigma_{xyT}} - {\sigma_{yzT}\left( {\sigma_{xxT} - \sigma_{i}} \right)}}} \\{C_{i} = {{\left( {\sigma_{yyT} - \sigma_{i}} \right)\left( {\sigma_{xxT} - \sigma_{i}} \right)} - \sigma_{xyT}^{2}}}\end{matrix}\left( {{i = 1},2,3} \right)};} \right. & (8)\end{matrix}$ in the formula: σ_(xx) is an induced stress produced bythe hydraulic fracture in an original maximum horizontal crustal stressdirection (parallel to an x-axis direction), and a specific first stressvalue at each point is σ_(xx) ^(i), MPa; σ_(yy) is an induced stressproduced by the hydraulic fracture in an original vertical crustalstress direction (parallel to a y-axis direction), and a specific secondstress value at each point is σ_(yy) ^(i), MPa; σ_(zz) is an inducedstress produced by the hydraulic fracture in an original minimumhorizontal crustal stress direction (parallel to a z-axis direction),and a specific third stress value at each point is σ_(zz) ^(i), MPa;σ_(xy), σ_(xz), and σ_(yz) are shear induced stresses produced by thehydraulic fracture, and a specific forth stress value at each point isσ_(xy) ^(i), σ_(xz) ^(i), σ_(yz) ^(i) respectively, MPa; P is a porepressure in the stratum after leak-off of fracturing fluid, and aspecific fifth stress at each point is P^(i), MPa; Δσ is a pore elasticstress in the stratum after leak-off of fracturing fluid, and a specificsixth stress value at each point is Δσ^(i), MPa; σ_(h) is an originalminimum horizontal crustal stress, MPa; σ_(H) is an original maximumhorizontal crustal stress, MPa; σ_(V) is an original vertical crustalstress, MPa; o_(i)(i=1, 2, 3) is the magnitude of the three-directionprinciple effective stress in the reservoir space after the first,second and third induced stress fields are overlapped with the originalcrustal stress field, where σ1>σ2>σ3, MPa; β_(xi), β_(yi), and β_(zi)(i=1, 2, 3) are included angles between respective directions ofeffective principal stress σ_(i)(i=1, 2, 3) in the reservoir space afterfirst, second and third induced stress fields are overlapped with theoriginal crustal stress field and the x-axis direction, the y-axisdirection and the z-axis direction respectively, 0° to 90°.
 6. Themethod for predicting the reservoir reform volume after vertical wellvolume fracturing of the low-permeability oil/gas reservoir according toclaim 1, wherein in Step (5), the open fracturing determinationcoefficient M of the natural fracture in the reservoir space and theshear fracturing area determination coefficient S of the naturalfracture are calculated so as to predict the reservoir reform volumeafter the volume fracturing, the process is as follows: $\begin{matrix}\left\{ {\begin{matrix}{M = {- \sigma_{n}}} \\{\sigma_{n} = {{\left( {{\sigma_{2}\cos^{2}\theta} + {\sigma_{3}\sin^{2}\theta}} \right)\sin^{2}\phi} + {\sigma_{1}\cos^{2}\phi}}} \\{\phi = {\arccos \left( {n_{1},{nf}} \right)}} \\{\theta = {\arctan \left( \frac{\cos \left( {n_{3},{nf}} \right)}{\cos \left( {n_{2},{nf}} \right)} \right)}} \\{{\cos \left( {n_{i},{nf}} \right)} = {{\cos \; \beta_{xi}\sin \; {\alpha sin\vartheta}} + {\cos \; \beta_{yi}\cos \; \alpha} + {\cos \; \beta_{zi}\sin \; {\alpha cos\vartheta}}}}\end{matrix}\left( {{i = 1},2,3} \right)} \right. \\{\mspace{79mu} \left\{ {\begin{matrix}{S = {\tau - {k_{f}\sigma_{n}} - \sigma_{o}}} \\{\tau = \sqrt{{\left( {{\sigma_{2}^{2}\cos^{2}\theta} + {\sigma_{3}^{2}\sin^{2}\theta}} \right)\sin^{2}\phi} + {\sigma_{1}^{2}\cos^{2}\phi} - \sigma_{n}^{2}}}\end{matrix};} \right.}\end{matrix}$ in the formula: σ_(n) is a positive stress of a naturalfracture wall, MPa; ψ is an included angle between a normal vector of anatural fracture surface and a maximum effective principal stress σ_(i)after the stress fields are overlapped, 0⁰ to 90°; θ is an includedangle between the normal vector of the natural fracture surface and aminimum effective principal stress σ₃ after the stress fields areoverlapped, 0° to 90°; α is an included angle between an inclinationangle of the natural fracture, which is, between the normal vector ofthe natural fracture surface and a y-axis, 0° to 90°; ϑ is an includedangle between the natural fracture trend and an original maximumhorizontal crustal stress (an x-axis direction), 0° to 90°; σ is a shearstress suffered by the natural fracture surface, MPa; K_(f) is afriction coefficient of the natural fracture wall, no dimension; σ_(o)is a cohesive force of the natural fracture, Mpa; a total swept volumeof S>0 and M>0 in the reservoir space is the reservoir reform volumeafter vertical well volume fracturing.